Lepton Flavor Violation and Local Lepton Number

TL;DR

This work analyzes a minimal theory of neutrino masses based on a locally gauged lepton-number symmetry $U(1)_\ell$ broken at a low scale, which yields a dark-matter candidate and a new gauge boson $Z_\ell$. Anomaly cancellation requires four new fermions, whose masses arise from the symmetry breaking, and the model predicts Dirac neutrinos and distinctive collider signatures. Lepton flavor violation arises at one loop via the exchange of the new charged fermions and a neutral scalar, with key processes $\mu \to e \gamma$, $\mu \to 3e$, and $\mu \to e$ conversion studied as functions of a small set of Yukawa couplings $\lambda_{e,\mu,\tau}$ and masses $(M_\Psi, M_\phi)$; current bounds push TeV-scale masses for $\mathcal{O}(0.1-1)$ couplings, while future experiments will probe sizable regions of parameter space and test correlations with dark matter and collider signals. The analysis highlights that combining LFV searches with collider and dark-matter constraints provides a powerful, testable framework for the origin of neutrino masses and lepton-number violation at accessible energy scales.

Abstract

We investigate the predictions for lepton number violating processes within the minimal theory of neutrino masses based on the spontaneous breaking of local lepton number. In this framework, the symmetry is broken at the low scale, leading to the existence of a viable dark matter candidate. The new fermions required for anomaly cancellation mediate lepton number violating processes at the one-loop level. We present a detailed calculation of the most relevant processes, including $μ\to e γ$, $μ\to 3 e$, and $μ\to e$ conversion in nuclei. The regions of parameter space excluded by current experimental bounds are identified, and we emphasize the interplay between collider observables and charged lepton flavor violating signatures as a key test of this minimal theory of neutrino masses.

Figures (8)

• Figure 1: One-loop Feynman diagram for $\mu \to e \gamma$.
• Figure 2: In the upper panel we show the branching ratio for $\mu \to e \gamma$ vs. $M_{\Psi}$ for different values of $\lambda_e$ and $\lambda_\mu$. The red region is excluded by the MEG II experiment bounds afanaciev2025newlimitmuegammadecay and the dashed red line shows the projected MEG II bound Baldini_2021. Here we assume $M_\Psi=2 M_\phi$. In the lower panel we show the allowed parameter space in the $M_\Psi -M_\phi$ plane for different values of $\lambda_e$ and $\lambda_\mu$. The shaded regions are excluded by MEG II afanaciev2025newlimitmuegammadecay.
• Figure 3: As in Fig. \ref{['fig:mutoegamma']} we show the shaded region excluded by the BABAR experiment Aubert_2010. In the upper panel, we show the impact of the experimental bounds on the ${\rm{BR}}(\tau \to e \gamma)$, while in the lower panel, we show the results for ${\rm{BR}}(\tau \to \mu \gamma)$. The green dashed line shows the projected Belle II sensitivity Belle-II:2018jsg.
• Figure 4: Feynman diagram of the photon contribution for $\mu$ to e conversion.
• Figure 5: In the upper-panel we show the prediction for the branching ratio of $\mu \to e$ conversion in Al. The red and blue dashed lines show the projected bounds by the COMET and Mu2e experiments COMET:2025sdw, respectively. The lower-panel shows the predictions for $\mu \to e$ in Gold. The blue shaded region is excluded by the SINDRUM II experiment SINDRUMII:2006dvw.